The Cohomology of Nilpotent Lie Algebras and Its Generating Functions

Abstract

By making use of the recently measured spin-wave dispersion relations we have calculated the spin-wave contributions to the low-temperature specific heats of antiferromagnetic MnF2, FeF2, CoFz and NiFz from 0 to 50 OK (0 to 35 OK for CoF2) using two different numerical methods. T h e results are compared with the experimental measurements of Stout and Catalano for temperatures of 1 5 OK and above; it is suggested that further experimental measurements below 15 'K would b e worth while.

Lie groups

“…In [184] one has obtained a condition for the triviality of the group H~(G, V) of the one-dimensional cohomologies of the Lie group G with an Abelian radical with coefficients in the G-module V. The cohomology of semisimple Lie algebras with coefficients in Verma modules are investigated in [319] where one proves their finite-dimensionality and nontriviality. A method of the computation of the cohomology H*(g, V) of a nilpotent Lie algebra ~ with values in an ~-module V, where ~=~acg, ~ is a semisimple commutative subalgebra in ~, complementary to the ideal g , is presented by Tolpygo [103].…”